A new magnetic field dependence of Landau levels on a graphene like structure

Abstract

We consider a tight-binding model on the honeycomb lattice in a magnetic field. For special values of the hopping integrals, the dispersion relation is linear in one direction and quadratic in the other. We find that, in this case, the energy of the Landau levels varies with the field B as E_n(B) ~ [(n+γ)B]^{2/3}. This result is obtained from the low-field study of the tight-binding spectrum on the honeycomb lattice in a magnetic field (Hofstadter spectrum) as well as from a calculation in the continuum approximation at low field. The latter links the new spectrum to the one of a modified quartic oscillator. The obtained value $\gamma =1/2$ is found to result from the cancellation of a Berry phase.

4 pages, 4 figures

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• Electric Field Effect in Atomically Thin Carbon Films
• Landau level spectroscopy of ultrathin graphite layers
• Zero modes of tight binding electrons on the honeycomb lattice
• BCS-BEC crossover on the two-dimensional honeycomb lattice
• Quantum Hall effect and the topological number in graphene

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